Glencoe Math: Course 3, Volume 2
GM
Glencoe Math: Course 3, Volume 2 View details
4. Properties of Similar Polygons
Continue to next subchapter

Exercise 5 Page 549

Practice makes perfect
We are given two similar quadrilaterals and we want to find the area of both figures.

We can see that both figures are rectangles. The area of a rectangle is calculated by multiplying the rectangle's length, l, times its width, w. A = l w To calclate the area of the Figure 1, we substitute 12 for l, and 8, for w.

A = l w
A = ( 12)( 8)
A = 96

Now, we can substitute 21 for l and 14 for w, and find the area of Figure 2.

A = l w
A = ( 21)( 14)
A = 294

The area of Figure 1 is 96 and the area of Figure 2 is 294.

We want to compare the scale factor of the side lengths and the ratio of the areas. A scale factor is the ratio of the lengths of two corresponding sides of two similar polygons. Let's find the scale factor!

JM/AD
14/8
7/4
In Part A, we found that the area of Figure 1 is 96 and the area of Figure 2 is 294. To find the ratio of the areas, we will divide the area of Figure 2 by the area of Figure 1.

294/96
â–¼
Simplify
21* 14/12* 8
3* 7 * 2* 7/2 * 2 * 3 * 8
3* 7 * 2* 7/2 * 2 * 3 * 8
7 * 7/2* 8
49/16

To compare the fractions 74, and 4916, let's calculate a square of 74.

(7/4)^2

Write power as a product

7/4 * 7/4
7* 7/4* 4
49/16

We can see that the ratio of areas is a scale factor of side lengths squared.